On 3/13/2011 9:52 AM, Jason Resch wrote:

On Sun, Mar 13, 2011 at 7:24 AM, Evgenii Rudnyi <use...@rudnyi.ru <mailto:use...@rudnyi.ru>> wrote:

    on 13.03.2011 08:29 Jason Resch said the following:

        On Sat, Mar 12, 2011 at 6:07 AM, Stathis
        Papaioannou<stath...@gmail.com <mailto:stath...@gmail.com>>wrote:

            On Tue, Mar 8, 2011 at 9:45 PM, Andrew
            <mailto:andrewsol...@gmail.com>> wrote:

                So, 'first person indeterminacy' simply means that I
                don't know
                what observation I will make next?

            It is not just ignorance, it is true indeterminacy. Even
            if you
            have all the information you cannot know which observation
            you will
            make next.

            -- Stathis Papaioannou

        To add to Bruno's and Stathis's point, first person indeterminacy,
        even when the details of the experiment are known, is an essential
        piece of the Sleeping Beauty Problem:

    Do I understand correctly that first person indeterminacy means
    that there is for example not zero probability for the next event.

    I go along the street. Someone runs to me and injects some
    sleeping drug, then she puts me into the bag, and after some
    indefinite period of time I wake up in an unknown place.

    Is there some other meaning that I have missed?


If you could be surreptitiously injected with a sleeping drug that immediately caused a loss of consciousness, then there is a non-zero probability that in your next conscious moment you will find yourself awaking in some room. Perhaps a meteor falls from space and hits you on the head, and the next thing you know you are in a hospital bed awaking from a coma. Even if the probability of this happening is 1 in a trillion, there is some probability your next moment of awareness won't be here and now but there and then. The other part of indeterminacy arises when you awake. Are you in hospital A or hospital B? You might be in a white windowless room, and from your perspective and knowledge either is a valid possibility with a non-zero probability, but once you are told, then an entire consistent history "collapses", your neighbor heard a bang and saw fire on your roof, he called the fire department, they found you unconscious and an ambulance took you to hospital X, where you remained for some time before you awoke.

These examples are not quite as interesting since they don't involve duplication (of either yourself or your conscious state). In the sleeping beauty problem where she is awoken on both Monday and Tuesday, in effect her identical conscious state is duplicated across two times, this is analagous to duplicating her conscious state in two different times. E.g., Beauty is told she will be destroyed, then a teleporting machine will re-create her in hospital A and hospital B, she won't know which hospital she is in. Now consider how this is similar to the teleporting recreating her state on Monday, then it destroys her and on Tuesday recreates her again and destroys her. When she emerges from the teleporting machine (whether in a different place or a different time) she won't know which day it is, and has at best a 50% probability of correctly guessing. Being in the same place at two different times is no stranger than being at two different places in the same time, we just aren't used to it because teleporting machines do not exist.

Assuming the universe is infinitely large (as the latest theories of cosmic inflation suggest), and assuming that there is a finite number of states a volume of space can be in (as suggested by the holographic principal) then your conscious state recurs an infinite number of times, just like any finite string of digits does in Pi. You are in different places at the same time (or different times, it doesn't matter) and we are always at all times involved in some giant sleeping beauty problem (or comp duplication experiment). We have no ability to guess where we are now, or where we will be in the next moment. Consider the possibility of an oscillatory universe, with a finite number of possible states. As many as 50 billion years might separate each collapse/big bang cycle, however given the finite number of possible states, the cycles will inevitably repeat. It might be 10^10^100 collapse cycles before Earth, and you reappear; an unimaginably large amount of time, but your next conscious moment is just as likely to be that future self, as it is the one in this time. If you enter a duplicator and are destroyed and then recreated 1 year from now, or a billion years from now, it seems like no time at all, regardless of how long it is. The same is true for being duplicated across distances. If eternal inflation is true, you might exist somewhere 10^10^100 meters from here, and your next conscious moment could "leap" to that location. It is easier to see this leaping occur intuitively if you imagine yourself destroyed in one location, but as Bruno's steps show, this destruction is not necessary.


But there is a problem with this. In fact our world is quite predictable. This is because we are quasi-Newtonian beings - our actions and thoughts are associated with (infinitely?) large classes of microscopic quantum events that are indistinguishable at our level. It is only when a microscopic quantum event is amplified to the quasi-classical level that "our" world splits. Of course this may happen many times over a life-time, but then the "you" in the split off world is not the same person - they have the same history up to some point, but then they have different experiences and become different persons with different thoughts and memories. The giant sleeping beauty problem is no more than the uncertainty in predicting our future - which we knew anyway.


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